Related papers: Dual-Select FMA Butterfly for FFT: Eliminating Twi…
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of…
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
The need for wireless communication has driven the communication systems to high performance. However, the main bottleneck that affects the communication capability is the Fast Fourier Transform (FFT), which is the core of most modulators.…
Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the…
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…
The need for wireless communication has driven the communication systems to high performance. However, the main bottleneck that affects the communication capability is the Fast Fourier Transform (FFT), which is the core of most modulators.…
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of…
Fast transforms correspond to factorizations of the form $\mathbf{Z} = \mathbf{X}^{(1)} \ldots \mathbf{X}^{(J)}$, where each factor $ \mathbf{X}^{(\ell)}$ is sparse and possibly structured. This paper investigates essential uniqueness of…
Fast Fourier transform (FFT) of large number of samples requires huge hardware resources of field programmable gate arrays (FPGA), which needs more area and power. In this paper, we present an area efficient architecture of FFT processor…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
This paper is concerned with the fast computation of Fourier integral operators of the general form $\int_{\R^d} e^{2\pi\i \Phi(x,k)} f(k) d k$, where $k$ is a frequency variable, $\Phi(x,k)$ is a phase function obeying a standard…
Fast Fourier Transform (FFT) libraries are widely used for evaluating discrete convolutions. Most FFT implementations follow some variant of the Cooley-Tukey framework, in which the transform is decomposed into butterfly operations and…
The "all-or-nothing" clause evaluation strategy is a core mechanism in the Tsetlin Machine (TM) family of algorithms. In this approach, each clause - a logical pattern composed of binary literals mapped to input data - is disqualified from…
Parker and L\^e introduced random butterfly transforms (RBTs) as a preprocessing technique to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure restricts the dimensions of the matrix. Furthermore,…
Interleaved Frequency Division Multiple Access (IFDMA) has the salient advantage of lower Peak-to-Average Power Ratio (PAPR) than its competitors like Orthogonal FDMA (OFDMA). A recent research effort put forth a new IFDMA transceiver…
In this paper, an optimized efficient VLSI architecture of a pipeline Fast Fourier transform (FFT) processor capable of producing the reverse output order sequence is presented. Paper presents Radix-2 multipath delay architecture for FFT…
Two-dimensional Fourier transform plays a significant role in a variety of image processing problems, such as medical image processing, digital holography, correlation pattern recognition, hybrid digital optical processing, optical…